The following is my line-by-line analysis of the covert rhetorical techniques used in the entire paragraph.

The author's entire bias is buried in rhetoric throughout the paragraph. The paragraph includes complications and introduces ambiguities. One might consider this poor style if they did not recognize it as advanced rhetoric. First consider:

Friendship is not a subject we give a lot of thought to.

Note the presumptuous and indirect use of "we give" rather than a more direct "you do not give". Also note the use of "not" being placed further away from the the verb. Compare with the following:

Friendship is a subject you do not give a lot of thought to.

Clearly, the original sentence is more easily acceptable to a reader. The next sentence is rhetorical:

As the saying goes, we know who our friends are.

Is there really such "a saying"? One could just as easily say, "As the saying goes, we only know who our friends are when the going gets tough." The next sentence introduces a false "we've probably never considered" along with an arbitrary statement:

But we've probably never considered the difference between, say, "convenience friends" and "crossroads friends."

The "but" is an empty segue that only seems to make sense. This is a false "we've probably never" because the referenced author is the one who is defining the difference. It would be like someone introducing Einstein's seminal paper with "we've probably never considered the theory of relativity...but Einstein has...". The word "say" hides a carefully crafted and deliberately persuasive point within an informal, impromptu voice. And the final statement is the target statement:

Judith Viorst has, and the classification of friends she outlines here will probably ring true to you.

The sentence is understood as follows:

"Judith Viorst has [considered the difference], and the classification of friends she outlines here will probably ring true to you.

Grammatically, it's similar to the following:

"Did you eat the pie?"

"I did, and it was delicious."

This statement "sneaks in" the "fact" that Judith has considered such a "marvelous thought" that "the rest of us dummies never thought about". All of that within a single word: "has". That "fact" is quickly buried in complexity and ambiguity, so by the time you figure out what it means, you can forget that the author said something questionable. In other words, the author's writing is highly rhetorical, and she is hiding the rhetoric with complexity and ambiguity.

This is not necessarily "bad". In fact, it's quite an impressive study in the use of effective, covert rhetoric. This construction is idiomatic of positive book reviews as well as book-selling copy on both the back cover and front jacket flap.

The usual wording of this idiom is "the pot calling the kettle black". The idea is that the pot is black itself, so it is not in the position of being able to accuse the kettle of being black. A very similar idiom you will probably be familiar with is "he who lives in a glass house shouldn't throw stones [at others]", or any variations thereof. Wikipedia has more similar idioms still.

The pot-kettle situation is a shorthand to refer to that idiom. It is not a common shorthand, so you won't find it in a dictionary. It is just a hint by this particular author at the actual idiom.